Question: Which of the following numbers is a factor of 136? ${5,8,10,12,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $136$ by each of our answer choices. $136 \div 5 = 27\text{ R }1$ $136 \div 8 = 17$ $136 \div 10 = 13\text{ R }6$ $136 \div 12 = 11\text{ R }4$ $136 \div 14 = 9\text{ R }10$ The only answer choice that divides into $136$ with no remainder is $8$ $ 17$ $8$ $136$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $136$ $136 = 2\times2\times2\times17 8 = 2\times2\times2$ Therefore the only factor of $136$ out of our choices is $8$. We can say that $136$ is divisible by $8$.